For example, when reading piano music on a grand staff, I know that if there is an A# in the treble clef staff (where it's normally natural), it changes all of the A's in the rest of that measure to A#.

Do all of the As in the bass clef staff stay natural unless they also have a # symbol next to them, or are they all affected by the # in the treble clef?

4 Answers
4

The answer to the question in the title of your post is, "it depends." As a general rule for Western notation as it is practiced in the United States, the answer would be "no"; not only is each staff independent with respect to accidentals, each octave is independent with respect to accidentals. However, when an accidental is present in one staff but missing from another, and the accidental is not merely cautionary as in your example, a misprint is likely unless you know that such a "clash" is within the style of the piece. The same applies to an accidental missing from one octave of a staff. Within a staff, however, in some French publications, an accidental applied to one octave is intended to apply to all octaves. This phenomenon appears with some frequency in the "classical" saxophone literature. I would expect different staves still to be independent in this case, but again, misprints are possible.

You may need to distinguish between accidentals and sharps and flats that belong to the key. If the key is D sharp then that is the key for all the clefs in a specific bar. There may be some reasons that notes are raised or lowered that fall outside issues regarding key.

There may be some chromatic passing notes that may very easily have sharps or flats in them that do not signify a change of key. They may also be specific to a clef and not necessarily happen on all the clefs / voices of a piece.